Question

1. find the distance between the points (-7,8) and (3,-4).

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Here, $x_1=-7,y_1 = 8,x_2=3,y_2=-4$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=3-(-7)=3 + 7=10$.
$y_2 - y_1=-4 - 8=-12$.

Step3: Square the differences

$(x_2 - x_1)^2=10^2 = 100$ and $(y_2 - y_1)^2=(-12)^2=144$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=100 + 144=244$.

Step5: Take square - root

$d=\sqrt{244}=\sqrt{4\times61}=2\sqrt{61}$.

Answer:

$2\sqrt{61}$